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Transition density of an infinite-dimensional diffusion with the jack parameter
Published online by Cambridge University Press: 16 January 2023
Abstract
From the Poisson–Dirichlet diffusions to the Z-measure diffusions, they all have explicit transition densities. We show that the transition densities of the Z-measure diffusions can also be expressed as a mixture of a sequence of probability measures on the Thoma simplex. The coefficients are the same as the coefficients in the Poisson–Dirichlet diffusions. This fact will be uncovered by a dual process method in a special case where the Z-measure diffusions are established through an up–down chain in the Young graph.
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust
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